# Is the Lorentz law incompatible with special relativity?

Charge-magnet paradox: the point electric charge q and the point magnetic dipole to its right are separated by distance d in the x’y’z’ frame. An observer in the x’y’z’ frame sees no torque, but a stationary observer in the xyz frame watching the x’y’z’ system move with constant velocity along the z axis sees the moving electric charge exert a torque on the moving magnet. Image credit: Mansuripur. ©2012 American Physical Society

The laws of classical electromagnetism that were developed in the 19th century are the same laws that scientists use today. They include Maxwell’s four equations along with the Lorentz law, which describes the force exerted by electric and magnetic fields on charged particles. But Masud Mansuripur, a professor of Optical Sciences at The University of Arizona in Tucson, is now arguing that the Lorentz law of force is incompatible with special relativity and momentum conservation, and should be abandoned. In a recent issue of Physical Review Letters, he has suggested replacing the Lorentz law with a more general expression of electromagnetic force density, such as one developed by Albert Einstein and Jakob Laub in 1908.

However, Mansuripur’s bold claim of a paradox with the Lorentz law has generated some intense criticism. One critic, Daniel Vanzella, a physics professor at the University of Sao Paulo in Sao Carlos, Brazil, has submitted a comment to Physical Review Letters arguing that the Lorentz law is perfectly compatible with special relativity, and that Mansuripur has misunderstood relativistic mechanics. The only paradox, Vanzella says, is why the high-ranking journal accepted the paper in the first place.

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